If p^x = q^y = r^z , where x , y and z are in GP, then consider the following statements: I. p , q and r are in AP. II. p , q and r are in GP. Which of the statements given above is/are correct?

Step-by-step solution

Let p^x = q^y = r^z = k Taking natural logarithm on all sides: x p = y q = z r = k x = k p , y = k q , z = k r Since x , y , and z are in GP, y^2 = xz Substituting the values of x , y , and z : ( k q )^2 = ( k p ) ( k r ) 1 ( q)^2 = 1 p r ( q)^2 = p r This implies that p , q , and r are in GP. Statement II is correct, while Statement I is not necessarily true. Answer: II only